A delta white noise functional

The additive renormalization% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabs7adaWgaaWcbaGaaeySdiaab6cacaqG0bqefeKCPfgBaGqb% diaa-bcaaeqaaOGaeyypa0Jaa8hiaiaacIcacaaIYaGaeqiWdaNaai% ykamaaCaaaleqabaGaeyOeI0IaaGymaiaac+cacaaIYaaaaGqadOGa% a4hiaiGacwgacaGG4bGaaiiCaiaacIcacqGHsislcaqGXoWaaWbaaS% qabeaacaqGYaaaaOGaai4laiaaikdacaGGPaGaa4hiaiaacQdaciGG% LbGaaiiEaiaacchacqGHXcqSdaWadiqaaiabgkHiTiaadkeacaGGNa% GaaiikaiaadshacaGGPaWaaWbaaSqabeaacaaIYaaaaOGaai4laiaa% ikdacaGFGaGaey4kaSIaa4hiaiaabg7acaWGcbGaai4jaiaacIcaca% WG0bGaaiykaaGaay5waiaaw2faaiaacQdaaaa!6C5C!\[{\rm{\delta }}_{{\rm{\alpha }}{\rm{.t}} } = (2\pi )^{ - 1/2} \exp ( - {\rm{\alpha }}^{\rm{2}} /2) :\exp \pm \left[ { - B'(t)^2 /2 + {\rm{\alpha }}B'(t)} \right]:\]is shown to be a generalized Brownian functional. Some of its properties are derived. is shown to be a generalized Brownian functional. Some of its properties are derived.On leave from Universidade do Minho, Area de Matematica, Largo Carlos Amarante, P-4700 Braga, Portugal.     

High-order harmonic generation with a strong laser field and an attosecond-pulse train: The Dirac-Delta comb and monochromatic limits

In recent publications, it has been shown that high-order harmonic generation can be manipulated by employing a time delayed attosecond-pulse train superposed to a strong, near-infrared laser field. It is an open question, however, which is the most adequate way to approximate the attosecond-pulse train in a semianalytic framework. Employing the strong-field approximation and saddle-point methods, we make a detailed assessment of the spectra obtained by modeling the attosecond-pulse train by either a monochromatic wave or a Dirac-Delta comb. These are the two extreme limits of a real train, which is composed by a finite set of harmonics. Specifically, in the monochromatic limit, we find the downhill and uphill sets of orbits reported in the literature, and analyze their influence on the high-harmonic spectra. We show that, in principle, the downhill trajectories lead to stronger harmonics, and pronounced enhancements in the low plateau region. These features are analyzed in terms of quantum interference effects between pairs of quantum orbits, and compared to those obtained in the Dirac-Delta limit.     

Production of recombinant bleaching enzymes from thermophilic microorganisms in fungal hosts

Cost-effective production of enzymes for industrial processes makes the appropriate selection of the host-vector expression system critical. We have developed two systems for the bulk production of bleaching enzymes from thermophiles. Kluyveromyces lactis has been developed as a secretion host employing expression vectors based on the 2μ-like plasmid pKD1 of Kluyveromyces drosophilarium. Our second system involves the filamentous fungus Trichoderma reesei. Fusion and nonfusion vectors have been constructed using the strong cellobiohydrolase 1 (cbh1) promoter. The KEX2 protease cleavage site and a 6 × HIS-tag have been incorporated to facilitate both cleavage and purification of the mature foreign proteins.     

Spectroscopic Studies on the Interaction of Tetramethylpyridylporphyrins and Cationic Clays

In the present work, the interaction between5,10,15,20-tetrakis(1-methyl-4-pyridyl)-21H,23H-porphine (TMPyP) and its metallated form(CoTMPyP) with three cationic clays was investigatedby X-ray diffraction (XRD), UV-VIS and resonance Ramanspectroscopies. Sodium montmorillonites K10 and KSFand a synthetic fluorohectorite (FHT) containingdifferent macrocycle loadings, were prepared by an ionexchange reaction. In nonsaturated KSF and FHT, theCoTMPyP molecule assumes a flat orientation, relativeto the host layers, giving rise to at least twoabsorption bands in the Soret region (ca. 445 and 465 nm)assigned to adsorbed and intercalated CoTMPyP,respectively. For the delaminated K10 sample, a broadband centered around 456 nm, indicates a majorcontribution from the metalloporphyrin on the clayexternal surfaces. The electronic spectra of FHTsamples containing increasing amounts of CoTMPyPshow bands red shifted even when a small amount ofporphyrin is used, suggesting that the electroniclevels of the macrocycle are more affected by theinteraction with the clay than by the metalloporphyrindistortion inside the galleries. The resonance Ramanspectra obtained for all CoTMPyP samples presentedonly minor shifts in peak positions and band width,with the exception of the FHT saturated sample, wherethe bands are clearly broader when compared to otherloadings, suggesting that porphyrin aggregation isoccurring. In the case of TMPyP, the bands at ca. 430and 468 nm were assigned to nonprotonated andprotonated molecules, respectively. This assignment issupported by resonance Raman spectroscopy, which alsoshowed the ₂ mode (ca. 1550 cm^-1) to bethe most sensitive peak to protonation.     

Additions of enantiopure alpha-sulfinyl carbanions to (S)-N-sulfinimines: asymmetric synthesis of beta-amino sulfoxides and beta-alphamino alcohols

The addition of the lithium anions derived from (R)- and (S)-methyl and -ethyl p-tolyl sulfoxides to (S)-N-benzylidene-p-toluenesulfinamide provides an easy access route to enantiomerically pure beta-(N-sulfinyl)amino sulfoxides. Stereoselectivity can be achieved when the configurations at the sulfur atoms of the two reagents are opposite (matched pair), thus resulting in only one diastereoisomer, even for the case in which two new chiral centers are created. The N-sulfinyl group primarily controls the configuration of the carbon bonded to the nitrogen, whereas the configuration of the alpha-sulfinyl carbanion seems to be responsible for the level of asymmetric induction, as well as for the configuration of the new stereogenic C-SO carbon in the reactions with ethyl p-tolyl sulfoxides. An efficient method for transforming the obtained beta-(N-sulfinyl)amino sulfoxides into optically pure beta-amino alcohols, based on the stereoselective non-oxidative Pummerer reaction, is also reported.     

Enzymatic bleaching of organosolv sugarcane bagasse pulps with recombinant xylanase of the fungus Humicola grisea and with commercial cartazyme HS xylanase

Organosolv (ethanol/water and acetosolv) pulps were treated with Humicola grisea var. thermoidea and compared with Cartazyme HS xylanase-treated pulp. The ethanol/water pulps treated with H. grisea had the same viscosity as unbleached pulps (8 cP). Ethanol/water pulps treated with Cartazyme had higher viscosity than H. grisea-treated pulps (12 cP). Acetosolv pulps treated with H. grisea and Cartazyme presented a reduction in viscosity; however, the pulps treated with H. grisea had a lower reduction in viscosity than Cartazyme-treated pulps. Ethanol/water pulps treated with H. grisea had a 23% reduction in kappa number in 4 and 8 h of treatment, compared with the unbleached pulps. Cartazyme-treated pulps had a kappa number similar to that of the control pulps for 4 h of treatment. Extending the treatment time to 12 h resulted in a reduction of 33%. The acetosolv pulp treated with H. grisea had a kappa number reduced to 23% in 4 h. Cartazyme treatment resulted in a reduction of 55 and 44% in kappa number for 4 and 8 h of treatment, respectively, when compared with control pulp. Extending the treatment time to 12 h decreased the kappa number 72%. Fourier transform infrared spectra and principal component analysis showed differences among unbleached, H. grisea-treated, and Cartazyme-treated pulps.     

A New ent‐Kaurane Diterpene from Stems of Alibertia macrophylla K. Schum. (Rubiaceae)

Phytochemical investigations of the stems of a specimen of Alibertia macrophylla led to the isolation and characterization of the new diterpene ent‐kaurane‐2β,3α,16α‐triol ( 1 ), along with triterpenes 2 – 8 , iridoids 9 – 12 , and phenolic acids 13 – 15 . The structure of 1 was established based on spectroscopic studies (¹H‐ and ¹³C‐NMR, IR, and HR‐ESI‐MS). This is the first report of the isolation of a diterpene from the Alibertia genus in Rubiaceae.     

(Z)-3-p-tolylsulfinylacrylonitrile as a chiral dienophile: diels-alder reactions with furan and acyclic dienes

The behavior of (Z)-3-p-tolylsulfinylacrylonitrile (1) as a chiral dienophile has been evaluated from its reactions with furan and acyclic dienes. Electrostatic interactions of the cyano group with the sulfinyl one restrict the conformational mobility around the C-S bond, thus controlling the pi-facial selectivity, which is almost complete in all cases, the approach of the diene from the less-hindered face of the dienophile (that bearing the lone electron pair) in the predominant rotamer being the favored one. The regioselectivity is also completely controlled by the cyano group. Additionally, the reactivity of compound 1 as well as its endo-selectivity are both higher than those observed for the corresponding (Z)-3-sulfinylacrylates, thus proving the potential of sulfinylnitriles as chiral dienophiles.